Fractional Modeling of Membrane Clogging

Abstract

Fractional Modeling of Membrane clogging Membrane filtration has become a key technology in water treatment, biotechnology, and various industrial applications, thanks to its efficiency, selectivity, and environmentally friendly operation. However, its performance is often limited by clogging, which leads to reduced permeate flux, higher energy consumption, and increased operational costs. Accurately modeling and predicting membrane clogging remain essential for improving the sustainability and efficiency of filtration processes. This thesis addresses this challenge through two complementary contributions based on fractional calculus. The first contribution focuses on developing and evaluating eight empirical fractional models to describe the evolution of permeate volume under different operating conditions. A hybrid optimization approach combining the Dragonfly Algorithm with nonlinear regression (DA–nlinfit) was used to estimate model parameters. The models achieved excellent predictive performance, with determination coefficients ranging from 0.9896 to 0.9997 and relative errors between 0.86% and 2.95%. These models offer accurate and flexible tools for simulating filtration dynamics, although they do not directly identify clogging mechanisms, which were inferred through additional analysis using Hermia’s equation.The second contribution introduces a new general fractional differential model (EDF), which represents a significant advance over classical Hermia-based models. Defined by three parameters (𝑛, 𝑘, 𝛼), the EDF model unifies classical and fractional formulations, reducing to Hermia’s models when 𝛼 = 1 and extending them for 𝛼 ≠ 1 to capture more complex dynamics. Validated theoretically and experimentally using three datasets representing different clogging mechanisms, the EDF model achieved superior accuracy (nRMSE between 0.93% and 1.73% and R² > 0.995) and allows the direct identification of the dominant clogging mechanism in a single step, overcoming the main limitations of classical approaches. Overall, this work demonstrates the power and versatility of fractional calculus for modeling membrane clogging. It bridges the gap between empirical accuracy and mechanistic insight, providing new mathematical tools to improve clogging analysis, process optimization, and the development of more efficient membrane filtration systems. Future perspectives include extending the EDF model to abnormal clogging behaviors, non-Newtonian fluids, and biological fouling phenomena.